Several problems exist in current frequency coherence signal processing apparatus and methods. First, at a particular frequency, multiple modes are sometimes indistinguishable from one another. The mode with the strongest frequency coherence can dominate the modes having weaker frequency coherence, such that the modes having weaker frequency coherence do not appear in the frequency coherence information or plots. A frequency coherence plot of such “masked” modes includes discontinuities. The modes appear to jump between frequencies. In addition, modes that are close together in slowness are blurred together and appear as a single mode.
One approach suggested for solving these problems in downhole measurement systems involves energy matching between receivers. Unfortunately, this solution is not feasible for use in logging-while-drilling tools. Even when used in wireline tools, such approaches can be problematic in the noisy environment encountered in a borehole.
Second, aliases can appear in frequency coherence information. Aliases make interpretation of the frequency coherence information difficult. Time- or domain or spatial aliasing can occur when the first peak of a signal on one receiver is matched with the second peak of the signal on another receiver. This aliasing yields a false slowness value for the signal. Arrival times and the character of the frequency coherence can be used to identify peaks that are aliases for the purpose of disregarding them. However, performing the operations necessary to identify aliases complicates the analysis.
A similar problem exists in the frequency domain. Since the velocity of the aliases is dependent upon the frequency of the mode, aliases appear in the frequency coherence information as curved modes. Again, while it is possible to identify and disregard these aliases, performing the operations necessary to identify frequency domain aliases complicates the analysis.
In both the time and frequency domains, aliases cause the depth-slowness-coherence plots to appear to have extra arrivals. Depth-slowness-coherence plots collapse the time or frequency out of the plot so that the information can be plotted on a depth basis. In such plots, extra arrivals need to be identified and disregarded for an analysis of the depth-slowness-coherence plot to produce the desired results.
Finally, analyzing modes across a broad frequency spectrum is difficult. Generating a broadband signal is not feasible in some environments, and current methods for processing signals produced by a simulated broadband signal are difficult to practice successfully. Current downhole measurement systems lack the power to generate broadband signals having sufficient power at all frequencies to produce a received signal having the required amplitude without quickly depleting the power source in the downhole measurement system. Combining received signals from multiple transmitter firings at near simultaneous times (so that there is minimal tool motion between firings) is difficult in the time domain. For example, in some downhole measurement systems, a signal having a center frequency of about five kilohertz is generated and a signal having a center frequency of about twelve kilohertz is generated less than about 100 milliseconds later. The data sets generated by these signals are currently processed separately. Attempts to combine these data sets to simulate a broadband signal in the time domain using time-slowness-coherence methods have not been entirely successful.